F is the restoring force, x the displacement, and k a particular constant of an oscillating system. The function that models the restoring force must be __________.
To determine the function that models the restoring force in an oscillating system, we can start by analyzing the given variables and their relationship.
In this scenario, F represents the restoring force, x represents the displacement, and k represents a particular constant. From this context, we can infer that the restoring force is directly proportional to the displacement. This indicates that the restoring force can be modeled by Hooke's Law.
Hooke's Law states that the restoring force (F) of an object is directly proportional to its displacement (x) and can be represented by the equation:
F = -kx
In this equation, k is the spring constant, also known as the stiffness coefficient, which quantifies the stiffness of the system. The negative sign indicates that the force is in the opposite direction of the displacement, emphasizing that it is a restoring force.
Therefore, the function that models the restoring force in this oscillating system is F = -kx, where F is the restoring force, x is the displacement, and k is the spring constant.